The UK can just re-use/roll-over the existing EU trade agreements

Some countries may well be willing to just carry over their trade deals to the UK on its own, but most will need to be at least partially renegotiated because they include numbers, such as quotas, that are shared between the EU as a whole. These numbers will need to be agreed for the UK individually, and the UK would now be in a numerically weaker negotiating position than when it is in the EU.

Most countries are much more likely to refuse to roll over their EU trade agreements because Brexit is seen as an opportunity for other nations to at least try to negotiate a better deal for themselves against a now weaker UK. With the UK's negotiating team that is likely to be overstretched renegotiating more than 50 free trade deals just to maintain the current level of deals, who can blame them for seizing the chance? Especially those countries that haven't been treated very well by the UK in the past.

These trade deals were signed on the understanding that the other countries were gaining better access to a market of more than 500 million people. They are unlikely to be prepared to make so many concessions for access to a market of just 65 million people.